Question: Solve for $x$ and $y$ using elimination. ${2x+3y = 26}$ ${-2x-5y = -34}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $2x$ and $-2x$ cancel out. $-2y = -8$ $\dfrac{-2y}{{-2}} = \dfrac{-8}{{-2}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {2x+3y = 26}\thinspace$ to find $x$ ${2x + 3}{(4)}{= 26}$ $2x+12 = 26$ $2x+12{-12} = 26{-12}$ $2x = 14$ $\dfrac{2x}{{2}} = \dfrac{14}{{2}}$ ${x = 7}$ You can also plug ${y = 4}$ into $\thinspace {-2x-5y = -34}\thinspace$ and get the same answer for $x$ : ${-2x - 5}{(4)}{= -34}$ ${x = 7}$